The article proposes a generic method to classify vertices or edges of a labeled graph. More precisely the method computes a confidence index for each vertex v or edge e to be a member of a target class by mining the topological environments of v or e. The method contributes to knowledge discovery since it exhibits for each edge or vertex an informative environnement that explains the found confidence. When applied to the problem of discovering strategic bonds in molecules, the method correctly classifies most of the bonds while providing relevant explanations to chemists. The developed algorithm GemsBond outperforms both speed and scalability of the learning method that has previously been applied to the same application while giving similar results.